Twenty tea party and conservative groups in Tennessee have signed onto a letter that asks Sen. Lamar Alexander to retire, claiming “our great nation can no longer afford compromise and bipartisanship, two traits for which you have become famous.”

Their letter praises Mr. Alexander, a Republican, for his long service to the Volunteer State.

But they say he has not fought hard enough for conservative ideals, even if it means digging in his heels when congressional gridlock calls for a deal.

“America faces serious challenges and needs policymakers who will defend conservative values, not work with those who are actively undermining those values,” they wrote.

Mr. Alexander is up for re-election in 2014, and his reelection website touts a comment from campaign co-chair Rep. John J. Duncan Jr., Tennessee Republican, that refers to Mr. Alexander as a “good Republican and good conservative who stands up for Tennesseans.”

So far, the tea party groups acknowledged, no viable competition has stepped forward to challenge the incumbent senator.

“When a serious contender eventually does enter the race, the moment their fundraising capability makes them a viable candidate, your re-election is in serious jeopardy,” they wrote. “Therefore, we urge you to conclude your long and notable career by retiring with dignity instead of fighting against a serious conservative primary challenger who would expose to all Tennessee voters the actual history of your voting record.”

Mr. Alexander’s office could not immediately be reached for comment on the letter.